His widow, Frances (pictured at the launch), the newsreader Trevor McDonald, and the Home Secretary Michael Howard joined together to invite applications from youngsters involved in race relations work, anti-crime and drugs schemes and other neighbourhood programmes.
Mr Howard said: "It is possible to take something positive and meaningful from this death of an exceptionally talented head teacher.
"We have a responsibility to teach every child the difference between right and wrong. Young people who do good work should be recognised," he said.
Philip Lawrence died in December 1995 when he was stabbed by a teenager, Learco Chindamo, outside St George's Catholic School, north-west London, as he tried to protect a pupil from a revenge attack.
After the conviction, Mrs Lawrence launched a "moral manifesto" against violence in society. Yesterday, she told young people at the launch in London: "I am sure you understand that I feel a little sad that my husband Philip is not here today.
"He would never have stood back from injustice, he would do everything he could to put it right. He was the strongest of men and the gentlest of men."
Cash prizes of up to pounds 1,000 will be presented on the anniversary of Mr Lawrence's death. Applications for the Home Office awards, which are open to young people aged 11-20, close in September.Reuse content